derivative of x/(3x)
Understand the Problem
The question is asking for the derivative of the function x/(3x), which can be simplified and differentiated using the rules of calculus.
Answer
The derivative is $0$.
Answer for screen readers
The derivative of the function is $0$.
Steps to Solve
- Simplify the Function First, we simplify the given function before finding its derivative. The function is
$$ f(x) = \frac{x}{3x}. $$
Simplifying it gives:
$$ f(x) = \frac{1}{3}. $$
- Differentiate the Simplified Function Now, we differentiate the simplified function. Since
$$ f(x) = \frac{1}{3}, $$
is a constant, its derivative is
$$ f'(x) = 0. $$
- State the Derivative Thus, the derivative of the original function
$$ f(x) = \frac{x}{3x} $$
is
$$ f'(x) = 0. $$
The derivative of the function is $0$.
More Information
In calculus, the derivative of a constant is always zero. Since the function simplifies to a constant value, the derivative reflects that no change occurs with respect to $x$.
Tips
- A common mistake is to forget to simplify the function first before differentiating. Ensure you simplify expressions wherever possible to avoid errors.
- Another mistake can be trying to differentiate a constant as if it were a variable function. Always remember the rule that the derivative of a constant is zero.